Counterexamples in Calculus
Published on 30. December 2010
Book
Paperback/Softback
101 pages
978-0-88385-765-6 (ISBN)
Description
Counterexamples in Calculus serves as a supplementary resource to enhance the learning experience in single variable calculus courses. This book features carefully constructed incorrect mathematical statements that require students to create counterexamples to disprove them. Methods of producing these incorrect statements vary. At times the converse of a well-known theorem is presented. In other instances crucial conditions are omitted or altered or incorrect definitions are employed. Incorrect statements are grouped topically with sections devoted to: Functions, Limits, Continuity, Differential Calculus and Integral Calculus. This book aims to fill a gap in the literature and provide a resource for using counterexamples as a pedagogical tool in the study of introductory calculus.
Reviews / Votes
This brief work is exactly as described, a collection of counterexamples from calculus. The book is organized into two parts. The first part is a list of 90 short statements grouped into five categories: ""Functions,"" ""Limits,"" ""Continuity,"" ""Differential Calculus,"" and ""Integral Calculus."" The second part is longer and includes counterexamples to each of the statements and well-known calculus theorems... Klymchuk provides an excellent reminder to calculus instructors and students of the need for rigor in calculus...In addition to helping calculus users to avoid complacency, this work provides wonderful illustrations of what can go wrong if one ignores the conditions placed on the theorems and rules of calculus. This book should be required reading for any long-term instructor of calculus."" - CHOICE MagazineMore details
Series
Edition
UK edition
Language
English
Place of publication
Washington DC
United States
Target group
Professional and scholarly
Product notice
Paperback (trade)
Unsewn / adhesive bound
Illustrations
112 b/w illus. 2 colour illus.
Dimensions
Height: 229 mm
Width: 154 mm
Thickness: 9 mm
Weight
167 gr
ISBN-13
978-0-88385-765-6 (9780883857656)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Dr Sergiy Klymchuk is an Associate Professor of the School of Computing and Mathematical Sciences at the Auckland University of Technology, New Zealand. He has 29 years of experience teaching university mathematics in different countries. He was born in Ukraine in 1958. Since 1996 he has lived in New Zealand. His PhD (1988) from Odessa National University, Ukraine was in differential equations. At present his main research interests are in mathematics education. He is a member of the Royal Society of New Zealand. He is also a member of a number of international groups in mathematics education including International Group for the Psychology in Mathematics Education (PME) and International Community of Teachers of Mathematical Modelling and Applications (ICTMA). Apart from Counterexamples in Calculus he also has written Paradoxes and Sophisms in Calculus as a supplementary resource to enhance teaching and learning of introductory calculus. He has more than 140 publications including three books on popular mathematics and science that have been, or are being, published in 11 countries: Money Puzzles, Science Puzzles and Shape Puzzles.
Content
Foreword; Introduction; Part I. Statements: 1. Functions; 2. Limits; 3. Continuity; 4. Differential calculus; 5. Integral calculus; Part II. Suggested Solutions: 6. Functions; 7. Limits; 8. Continuity; 9. Differential calculus; 10. Integral calculus; References.